Mix the flour, sugar, and walnuts in a large mixing bowl and combine thoroughly. Add ½ cup of milk, stir thoroughly, then slowly add the rest of the milk while stirring constantly to avoid forming lumps in the batter.

Grease a cake pan with 1 tablespoon of olive oil and pour in the batter. Drizzle the top of the batter with the remaining olive oil. Sprinkle the fresh rosemary evenly over the top of the cake.

Bake for about 45 minutes, or until a toothpick inserted in the center of the cake comes out clean.

While the cake is cooking, combine the lemons, sugar, and 1 cup of water in a small saucepan. Cook until the mixture is quite soft and bubbly, about 20 minutes.